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Dual clustering: integrating data clustering over optimization and constraint domains

機(jī)譯：雙重集群：在優(yōu)化和約束域上集成數(shù)據(jù)集群

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Spatial clustering has attracted a lot of research attention due to its various applications. In most conventional clustering problems, the similarity measurement mainly takes the geometric attributes into consideration. However, in many real applications, the nongeometric attributes are what users are concerned about. In the conventional spatial clustering, the input data set is partitioned into several compact regions and data points which are similar to one another in their nongeometric attributes may be scattered over different regions, thus making the corresponding objective difficult to achieve. To remedy this, we propose and explore in this paper a new clustering problem on two domains, called dual clustering, where one domain refers to the optimization domain and the other refers to the constraint domain. Attributes on the optimization domain are those involved in the optimization of the objective function, while those on the constraint domain specify the application dependent constraints. Our goal is to optimize the objective function in the optimization domain while satisfying the constraint specified in the constraint domain. We devise an efficient and effective algorithm, named Interlaced Clustering-Classification, abbreviated as ICC, to solve this problem. The proposed ICC algorithm combines the information in both domains and iteratively performs a clustering algorithm on the optimization domain and also a classification algorithm on the constraint domain to reach the target clustering effectively. The time and space complexities of the ICC algorithm are formally analyzed. Several experiments are conducted to provide the insights into the dual clustering problem and the proposed algorithm.
機(jī)譯：空間聚類由于其各種應(yīng)用而吸引了許多研究關(guān)注。在大多數(shù)常規(guī)聚類問題中，相似性度量主要考慮幾何屬性。但是，在許多實際應(yīng)用中，用戶所關(guān)注的是非幾何屬性。在傳統(tǒng)的空間聚類中，將輸入數(shù)據(jù)集劃分為幾個緊湊的區(qū)域，并且其非幾何屬性彼此相似的數(shù)據(jù)點可能會散布在不同的區(qū)域上，從而使相應(yīng)的目標(biāo)難以實現(xiàn)。為了解決這個問題，我們在本文中提出并探索了在兩個域上的一個新的聚類問題，稱為雙重聚類，其中一個域是指優(yōu)化域，另一個域是約束域。優(yōu)化域上的屬性是目標(biāo)函數(shù)優(yōu)化所涉及的屬性，而約束域上的屬性則指定依賴于應(yīng)用程序的約束。我們的目標(biāo)是在滿足約束域中指定的約束的同時，在優(yōu)化域中優(yōu)化目標(biāo)函數(shù)。我們設(shè)計了一種有效且有效的算法，稱為隔行聚類分類（Interlaced Clustering-Classification，簡稱ICC）來解決此問題。提出的ICC算法結(jié)合了兩個域中的信息，并在優(yōu)化域上迭代執(zhí)行聚類算法，并在約束域上迭代執(zhí)行分類算法，以有效地達(dá)到目標(biāo)聚類。正式分析了ICC算法的時間和空間復(fù)雜度。進(jìn)行了一些實驗，以提供對雙重聚類問題和提出的算法的見解。

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